Hello,
In order to reactivate the software with the new key please follow the steps below:
-open Parallels Desktop;
-in the menu line (Parallels Desktop, File, View etc.) click on "Parallels Desktop";
-choose "Activate Product";
-in the window that appears on the screen please change the old key to the new one.
Alternatively, you could wait till the trial period expires and the software asks you for the new key.